setmod_ff

setmod_ff([p|defpoly2])

setmod_ff([defpolyp,p])

setmod_ff([p,n])

:: Sets/Gets the current base fields.

return

number or polynomial

p

prime

defpoly2

univariate polynomial irreducible over GF(2)

defpolyp

univariate polynomial irreducible over GF(p)

n

the extension degree

• If the argument is a non-negative integer p, GF(p) is set as the current base field.
• If the argument is a polynomial defpoly2, GF(2^deg(defpoly2 mod 2)) = GF(2)[t]/(defpoly2(t) mod2) is set as the current base field.
• If the arguments are a polynomial defpolyp and a prime p, GF(p^deg(defpolyp)) = GF(p)[t]/(defpolyp(t)) is set as the current base field.
• If the arguments are a prime p and an extension degree n, GF(p^n) is set as the current base field. p^n must be less than 2^29 and if p is greater than or equal to 2^14, then n must be equal to 1.
• If no argument is specified, the modulus indicating the current base field is returned. If the current base field is GF(p), p is returned. If it is GF(2^n), the defining polynomial is returned. If it is GF(p^n) defined by setmod_ff(defpoly,p), [defpolyp,p] is returned. If it is GF(p^n) defined by setmod_ff(p,n), [p,defpoly,prim_elem] is returned. Here, defpoly is the defining polynomial of the n-th extension, and prim_elem is the generator of the multiplicative group of GF(p^n).
• Any irreducible univariate polynomial over GF(2) is available to set GF(2^n). However the use of defpoly_mod2() is recommended for efficiency.

[174] defpoly_mod2(100);
x^100+x^15+1
[175] setmod_ff(@@);
x^100+x^15+1
[176] setmod_ff();
x^100+x^15+1
[177] setmod_ff(x^4+x+1,547);
[1*x^4+1*x+1,547]
[178] setmod_ff(2,5);
[2,x^5+x^2+1,x]

References

section defpoly_mod2

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